Simplify the following expression: $z = \dfrac{-7n^2 - 49n + 210}{n - 3} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ z =\dfrac{-7(n^2 + 7n - 30)}{n - 3} $ Then we factor the remaining polynomial: $n^2 + {7}n {-30} $ ${-3} + {10} = {7}$ ${-3} \times {10} = {-30}$ $ (n {-3}) (n + {10}) $ This gives us a factored expression: $\dfrac{-7(n {-3}) (n + {10})}{n - 3}$ We can divide the numerator and denominator by $(n + 3)$ on condition that $n \neq 3$ Therefore $z = -7(n + 10); n \neq 3$